Yesterday I wrote a post in the Rajiv Gandhi International Airport in Hyderabad. I couldn’t post it there because I wasn’t connected, but Dubai airport had free wi-fi so I could finish the job a few hours later. The ICM interrupted a holiday I was having in the South of France with my wife’s family, so now, after a refreshing four-hour night, I find myself at 6.30am in the rather less glamorous Luton airport, stupidly early for a flight on a rather less glamorous airline than Emirates, with whom I flew to Hyderabad and back. Talking of stupid punctuality, there’s a maxim I quite like, which is probably very well known but I heard it only within the last year or two, which is that if you have never missed a plane then you spend too much of your life in airports. I like the maxim, but I don’t live by it, because I have an irrational dread of missing planes, and an entirely rational lack of dread of spending time in airports — if all else fails, they are a pretty good place to do mathematics. Today, all else has not failed, since I have a charged up computer (that’s an issue these days — I think my laptop is due a new battery) and multiple blog posts to write. I haven’t quite decided what form these will take: I cannot possibly write about days 2-4 in the same amount of detail as I have written about day 1, but once I start, it is hard to stop. So do I prefer to keep up the detail and risk stopping in the middle of day 2, or to force myself to become a bit sketchier? Perhaps I’ll be detailed, but more selective about what I write about.
It was never quite clear exactly when the bus would leave the hotel for the convention centre, so if I was short of sleep, I couldn’t afford to set my alarm so that I would have just enough time to catch it. So for me, each day of the ICM started with waking up earlier than I would like, and a little earlier than was strictly necessary. I’m not too fond of sleeping with air conditioning, so I would wake up feeling sticky and in definite need of a shower. The shower, I have to say, was one of the best hotel showers I can remember. Like many showers, it had a two-dimensional tap (one for temperature and one for amount of water), and once I had got the temperature to my liking on the first day, all I had to do on subsequent days was pull the little lever without rotating it and the water would be ready for me almost instantly, in generous quantities and at the same temperature that I had previously established. Once I was in a fit state to face the world, I would go downstairs to the lobby, ask about the bus and hear that I had time for breakfast. Breakfast was a buffet with Indian food in what I now know to be chafing dishes, of a kind that I would not normally feel like first thing but that I became used to. There was also more standard Western food available, but it wasn’t quite standard enough for me to feel tempted by it: for instance, there were croissants that were scaled down by a factor of about 3 in every direction that were a bit too pale and looked dry. There was also someone there cooking eggs — I had a couple of pretty good omelettes while I was there.
I was to come to knw the bus pretty well. As well as the driver, there would be one or two people who were either boys or very young men — the same people each time — who would shepherd us on. Even though the bus was pretty small, more like an outsized minibus, the driver was in a separate compartment at the front. To get into this compartment, there was a door that was strangely un-car-like: it was wooden with a window in it, and it was … well, just an ordinary door that opened on a hinge.
There were two things I was a little anxious about when I was in India. One was Delhi belly (after a lot of thought, I’ve given up on trying to think of a suitable Hyderabad equivalent). Every time I felt the smallest stomach twinge or hint of indigestion, I wondered whether this was the moment. And I know what I’m talking about here. In Beijing in 2002 I took a day off to go to an untouristy part of the Great Wall of China, which involved explaining to a taxi driver whose linguistic competence was disjoint from mine how to get to an obscure part of Beijing — not a bus station — from where the bus would leave. I got up stupidly early for that too, and then the bus didn’t leave for about an hour after the scheduled time. And a small way into the journey, but enough time for us to have reached a major traffic jam, I started to have serious worries about whether I would be able to last to our destination without a disastrous accident. Any more on that (and there is more) will probably be more information than you strictly need, so I’ll say merely that I did just make it, helped by the fact that we stopped off at a much less interesting place first. I think I may have been lucky and escaped from India without any illness, even minor. I was pretty careful when there, avoiding all salad and fresh fruit, drinking only bottled water, and so on.
My other worry was malaria, even though I had been told at my doctor’s surgery that this part of India was low risk (meaning that it wasn’t worth taking any medication). I had insect repellent with me, which was an unpleasant lotion that left my skin with a stickiness very similar to what I had removed in the shower. (It also stung if I put it on soon after shaving, which I did.) However, my first bus journey, the one to the opening ceremony, had taught me that there could be mosquitoes on buses. In fact, there were a few on every daylight bus journey I made (and possibly the ones after dark too, but those would have been harder to spot). They didn’t actually seem to be out to get me, even on the day that I did not wear repellent, but others later told me that they had been bitten a lot. (On the first day, I decided that it was worth looking ridiculous in order to lessen still further my tiny risk of malaria, so in the bus I wore my shirt collar up with the top button done up. I also pulled my socks as high up my legs as they would go.) I left India without a single bite, from which I deduce that I did not get malaria. And it’s getting to the point where I’m pretty sure I did not get any kind of stomach problem either. (The last few sentences are written from my destination in the south of France.)
The traffic was again not nothing but not dreadful and we arrived in good time, so I probably made straight for the “Internet Café,” which was all internet and no café. And I probably didn’t go to the main hall until just before 9.30 when the day’s events started, reasoning (based on my experiences of previous ICMs) that places there would be at far less of a premium than they had been for the opening ceremony. I was actually a bit hazy about what was going to happen, but Lovász helpfully told us: we were going to have some talks and videos about the life and work of Shiing-Shen Chern, in order to inaugurate his new prize. (It had been awarded to Nirenberg the previous day, but not enough song and dance had yet been made about the prize itself.)
Present there was May Chu, Chern’s daughter, and present in the way that the stars are present in the sky (in the sense that the light we see was emitted long ago) were Jim Simons, famous collaborator of Chern’s and endower of two thirds of the prize, and others. May Chu was completely Americanized (or rather her voice was — I don’t know how she lives), confident in a good way, and articulate. She also had interesting traces of Chern’s looks in her face, though I wouldn’t have noticed that had I not known in advance that she was his daughter. She told us that we would be seeing three short videos, one a communication from Jim Simons, one a biographical sketch of Chern, and one a series of reminiscences.
The first was the Jim Simons video. I won’t describe the whole thing but here are a few highlights. It began with Simons directly addressing us, saying the kind of thing you would expect, but most of it was an interview: Dennis Sullivan was called in to interview Simons about Chern, and between the two of them they managed to make it highly entertaining. Simons, by the way, looked about 60, with white hair and a short white beard. And you know those moments when you spot a striking resemblance between two people who don’t look like each other, some kind of Gestalt that you cannot analyse? I had that with Dennis Sullivan and Bill Murray. Does anyone else see it? Here is Dennis Sullivan and here is Bill Murray. (Of course, two pictures chosen fairly randomly from Google images won’t convey the similarity as well as actually seeing Sullivan moving and talking and having a mental image of Murray. Looking at the pictures though, I think the sloping eyebrows have something to do with it, together with the look of someone who has lived a lot of life, which I think they both have — I’m not talking about number of years.)
The video lasted about 15 minutes and you can watch it by going to the ICM home page, clicking on “online streaming activities” and choosing Day 2 Part 1 (and jumping forward a bit to get to it). But if you haven’t got time for that, then here are a few highlights. The first was Simons’s description of what it was like to see Chern for the first time. Simons had gone to Berkeley to do a PhD because of Chern, but for his first year Chern was on sabbatical. Then one day Simons was at a seminar and in walked a tall Chinese man with a large head (this point was emphasized in one of the other videos) who was clearly somebody. He asked who it was, and was amazed to discover that it was Chern: he had assumed that Chern was a shortening of something like Chernovsky. “Chen” would have suggested someone Chinese, but that extra “r” made all the difference to his perception.
When Sullivan asked whether Chern had been helpful to Simons when he was working on his PhD, he said a straight no, though qualified it by saying that Chern had been very encouraging. (I imagine this could be telling us that Simons was an independent thinker at an early stage.)
Sullivan told Simons that he had been to Chern’s talk at the ICM in Nice in 1970. Afterwards, he had gone up and asked Chern whether he could have his transparencies. Chern, who was completely uninterested in them, said of course he could. And apparently the only name mentioned on the transparencies was that of Simons, so now, 40 years later, Sullivan was going to give the transparencies to Simons.
As I mentioned in an earlier post, Simons is famous not just as a mathematician but also as somebody who left mathematics to set up a hedge fund, which he did so successfully that he is now one of the richest men in the world and a major philanthropist, with a particular interest in mathematical causes. Sullivan asked him how Chern had reacted on hearing that Simons would be leaving mathematics. Simons replied that Chern had never said anything critical to him about it, but that Chern had not heard the news in his presence, and that he, Simons, had heard about it later. Apparently, Chern said, “After all, he is not David Hilbert.”
Once the videos were over, Robert Bryant, the director of MSRI and a professor at Berkeley, gave a talk about the work of Chern. I don’t think I want to say that much about the talk, since there are much better ways of finding out about Chern’s work than reading an expansion of my notes on that talk. But that is not to say that I learnt nothing. For instance, though I had heard of Chern characters (since they are one of those concepts that becomes a buzzword, so that even if you are in another area and don’t know what they are, you know that they are central and important), I did not know the back story, so to speak, which is that they arose out of Chern’s (successful) efforts to find an intrinsic proof of the Gauss-Bonnet formula.
Before that, Bryant explained that Chern initially rose to prominence by being almost the only person in the world to understand something called the “method of equivalence,” which was invented by Elie Cartan. (Of course, Cartan himself understood it.) This caused me to reflect on how different the routes are by which mathematicians manage to prove theorems. Once Chern had understood Cartan’s method, he went on to find many deep applications of it. And there are several other stories like that. I don’t know how accurate it is, but the picture I have of Deligne is that he was at one time the only person who truly understood Grothendieck’s work, with spectacular consequences. But I know that I myself cannot work like that: I find it almost impossible to understand anything unless I already strongly feel the need for it, and can give myself the illusion that I am discovering it for myself. (Of course, it must be partly true that Chern was aware in advance of the kinds of problems that Cartan’s methods could help him with, but I still think that there is a distinction here.) This closes off large parts of mathematics to me, but leaves me with a niche where I can operate. And the subject is so big that a niche is all one needs.
I learned that Chern-Simons invariants are “secondary” invariants, in the sense that they are what you get when Chern classes vanish. As with what I learned about Ngo’s work, this is replacing one thing I don’t fully understand with some others, but that is nevertheless useful: the image is still blurred but less so than before.
At the end of the talk, Bryant told us that Chern had had 44 PhD students and 697 mathematical descendants (as of the 16th — Bryant suggested that after a couple of days one could no longer be sure that the figure was accurate).
The last note I wrote says, “Went way over time.” The effect of that was that what was supposed to be a measly 25-minute coffee break after almost two hours sitting in the same place became an even more measly coffee break of 15 minutes after exactly two hours sitting in the same place. Had I been in charge, I would have suggested starting the next talk (about the work of Nirenberg) a bit later, but perhaps that was not practical given that there might be people not present who would be coming to the later talk. It may sound trivial now, but this mattered: such were the queues for coffee that the difference between 25 minutes and 15 minutes was the difference between a cup of coffee and no cup of coffee. And after the night I had had, that meant the difference between feeling vaguely human and not feeling vaguely human.